Multifractal modeling of counting processes of long-range dependent network traffic

We study traffic streams through their counting process representation. We examine the long-range-dependent (LRD) characteristics of such processes. We first show that the measured LRD traffic, as described by the interarrival time and packet size sequences, is sufficiently well approximated by a synthesized stream formed by recording the counting state of the traffic at the start of each time slot. We then model these counting processes by constructing a multiplicative multifractal process. The model only contains two parameters. One is used to indicate the mean of the counting process; the other is employed to describe the variation of the traffic around the mean function. We show that this multifractal traffic characterization has well defined burstiness descriptors, and is easy to construct. We consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by properly parameterized multifractal processes. In comparing the system-size tail distributions, we demonstrate our model to effectively track the behavior exhibited by the system driven by the actual traffic processes.